Find the equation to the tangent to the curve x=cos(2y+pi) at (0, pi/4)

Normally to find a tangent we want to work out dy/dx, but since this equation is x=something, it's much easier to work out dx/dy first, then we get dy/dx by doing 1/(dx/dy)=dy/dx.
By the chain rule, dx/dy = -sin(2y+pi)2, since cos differentiates to -sin, and we need to remember to differentiate the bit in the brackets too, which is why we multiply by 2. Now let's substitute in our x and y values, and we get that dx/dy = -2sin(3pi/2) and (0, pi/4), which equals 2. So by using the little formula I gave earlier, we get dy/dx=1/2 here. So we know the tangent line has gradient 1/2, and passes through the point (0, pi/4), so we use the equation y=mx+c with m=1/2, which gives us c=pi/4, and the equation of the tangent line is y=1/2x + pi/4.

SJ
Answered by Sarah J. Maths tutor

10341 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How do we know which formulas we need to learn for the exam?


if f is defined on with f(x)=x^2-2x-24(x)^0.5 for x>=0 a) find 1st derivative of f, b) find second derivative of f, c) Verify that function f has a stationary point when x = 4 (c) Determine the type stationary point.


show that y = (kx^2-1)/(kx^2+1) has exactly one stationary point when k is non-zero.


1. (a) Find the sum of all the integers between 1 and 1000 which are divisible by 7. (b) Hence, or otherwise, evaluate the sum of (7r+2) from r=1 to r=142


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences